On the Brauer-Feit bound for abelian defect groups |
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Authors: | Benjamin Sambale |
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Institution: | 1. Mathematisches Institut, Friedrich-Schiller-Universit?t, 07743?, Jena, Germany
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Abstract: | We improve the Brauer-Feit bound on the number of irreducible characters in a $p$ -block for abelian defect groups by making use of Halasi and Podoski (Every coprime linear group admits a base of size two. http://arxiv.org/abs/1212.0199v1, 7]) and Kessar and Malle (Ann Math 178(2):321–384, 11]). We also prove Brauer’s $k(B)$ -Conjecture for 2-blocks with abelian defect groups of rank at most 5 and 3-blocks and 5-blocks with abelian defect groups of rank at most 3. |
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